LMFDB - Embedded newform 480.2.m.b.239.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [480,2,Mod(239,480)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(480, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("480.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 480 = 2^{5} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	480.m (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.83281929702$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 24x^{14} + 192x^{12} + 672x^{10} + 1092x^{8} + 880x^{6} + 352x^{4} + 64x^{2} + 4 $ x^16 + 24x^14 + 192x^12 + 672x^10 + 1092x^8 + 880x^6 + 352x^4 + 64*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.3
Root			$-3.49930i$ of defining polynomial
Character	$\chi$	$=$	480.239
Dual form			480.2.m.b.239.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30656 + 1.13705i) q^{3} +(-2.10100 + 0.765367i) q^{5} -2.27411 q^{7} +(0.414214 - 2.97127i) q^{9} -4.20201i q^{11} +3.21608 q^{13} +(1.87483 - 3.38896i) q^{15} +1.53073 q^{17} +4.82843 q^{19} +(2.97127 - 2.58579i) q^{21} +1.08239i q^{23} +(3.82843 - 3.21608i) q^{25} +(2.83730 + 4.35313i) q^{27} -1.74053 q^{29} -6.82843i q^{31} +(4.77791 + 5.49019i) q^{33} +(4.77791 - 1.74053i) q^{35} -7.76429 q^{37} +(-4.20201 + 3.65685i) q^{39} -2.46148i q^{41} -8.70626i q^{43} +(1.40385 + 6.55967i) q^{45} -1.08239i q^{47} -1.82843 q^{49} +(-2.00000 + 1.74053i) q^{51} -11.0866i q^{53} +(3.21608 + 8.82843i) q^{55} +(-6.30864 + 5.49019i) q^{57} +4.20201i q^{59} -8.48528i q^{61} +(-0.941967 + 6.75699i) q^{63} +(-6.75699 + 2.46148i) q^{65} -2.27411i q^{67} +(-1.23074 - 1.41421i) q^{69} +11.8851 q^{71} -4.54822i q^{73} +(-1.34523 + 8.55514i) q^{75} +9.55582i q^{77} -0.485281i q^{79} +(-8.65685 - 2.46148i) q^{81} -6.94269 q^{83} +(-3.21608 + 1.17157i) q^{85} +(2.27411 - 1.97908i) q^{87} +8.40401i q^{89} -7.31371 q^{91} +(7.76429 + 8.92177i) q^{93} +(-10.1445 + 3.69552i) q^{95} -10.9804i q^{97} +(-12.4853 - 1.74053i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{9} + 32 q^{19} + 16 q^{25} + 16 q^{49} - 32 q^{51} - 32 q^{75} - 48 q^{81} + 64 q^{91} - 64 q^{99}+O(q^{100}) $ 16 * q - 16 * q^9 + 32 * q^19 + 16 * q^25 + 16 * q^49 - 32 * q^51 - 32 * q^75 - 48 * q^81 + 64 * q^91 - 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/480\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$421$
$\chi(n)$	$-1$	$-1$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.30656	+	1.13705i	−0.754344	+	0.656479i
$3$	−1.30656	+	1.13705i	−0.754344	+	0.656479i
$4$		0			0
$5$	−2.10100	+	0.765367i	−0.939597	+	0.342282i
$5$	−2.10100	+	0.765367i	−0.939597	+	0.342282i
$6$		0			0
$7$	−2.27411			−0.859533			−0.429766	−	0.902940i	$-0.641404\pi$
$7$	−2.27411			−0.859533			−0.429766	+	0.902940i	$0.641404\pi$
$8$		0			0
$9$	0.414214	−	2.97127i	0.138071	−	0.990422i
$10$		0			0
$11$		−	4.20201i		−	1.26695i	−0.773762	−	0.633476i	$-0.781627\pi$
$11$		−	4.20201i		−	1.26695i	0.773762	−	0.633476i	$-0.218373\pi$
$12$		0			0
$13$	3.21608			0.891979			0.445990	−	0.895038i	$-0.352852\pi$
$13$	3.21608			0.891979			0.445990	+	0.895038i	$0.352852\pi$
$14$		0			0
$15$	1.87483	−	3.38896i	0.484079	−	0.875024i
$16$		0			0
$17$	1.53073			0.371257			0.185629	−	0.982620i	$-0.440568\pi$
$17$	1.53073			0.371257			0.185629	+	0.982620i	$0.440568\pi$
$18$		0			0
$19$	4.82843			1.10772			0.553859	−	0.832611i	$-0.313155\pi$
$19$	4.82843			1.10772			0.553859	+	0.832611i	$0.313155\pi$
$20$		0			0
$21$	2.97127	−	2.58579i	0.648384	−	0.564265i
$22$		0			0
$23$			1.08239i			0.225694i	0.993612	+	0.112847i	$0.0359971\pi$
$23$			1.08239i			0.225694i	−0.993612	+	0.112847i	$0.964003\pi$
$24$		0			0
$25$	3.82843	−	3.21608i	0.765685	−	0.643215i
$26$		0			0
$27$	2.83730	+	4.35313i	0.546038	+	0.837760i
$28$		0			0
$29$	−1.74053			−0.323208			−0.161604	−	0.986856i	$-0.551667\pi$
$29$	−1.74053			−0.323208			−0.161604	+	0.986856i	$0.551667\pi$
$30$		0			0
$31$		−	6.82843i		−	1.22642i	−0.789919	−	0.613211i	$-0.789878\pi$
$31$		−	6.82843i		−	1.22642i	0.789919	−	0.613211i	$-0.210122\pi$
$32$		0			0
$33$	4.77791	+	5.49019i	0.831727	+	0.955719i
$34$		0			0
$35$	4.77791	−	1.74053i	0.807614	−	0.294203i
$36$		0			0
$37$	−7.76429			−1.27644			−0.638221	−	0.769853i	$-0.720329\pi$
$37$	−7.76429			−1.27644			−0.638221	+	0.769853i	$0.720329\pi$
$38$		0			0
$39$	−4.20201	+	3.65685i	−0.672859	+	0.585565i
$40$		0			0
$41$		−	2.46148i		−	0.384418i	−0.981354	−	0.192209i	$-0.938435\pi$
$41$		−	2.46148i		−	0.384418i	0.981354	−	0.192209i	$-0.0615652\pi$
$42$		0			0
$43$		−	8.70626i		−	1.32769i	−0.747869	−	0.663846i	$-0.768923\pi$
$43$		−	8.70626i		−	1.32769i	0.747869	−	0.663846i	$-0.231077\pi$
$44$		0			0
$45$	1.40385	+	6.55967i	0.209273	+	0.977857i
$46$		0			0
$47$		−	1.08239i		−	0.157883i	−0.996879	−	0.0789416i	$-0.974846\pi$
$47$		−	1.08239i		−	0.157883i	0.996879	−	0.0789416i	$-0.0251541\pi$
$48$		0			0
$49$	−1.82843			−0.261204
$50$		0			0
$51$	−2.00000	+	1.74053i	−0.280056	+	0.243723i
$52$		0			0
$53$		−	11.0866i		−	1.52286i	−0.648250	−	0.761428i	$-0.724499\pi$
$53$		−	11.0866i		−	1.52286i	0.648250	−	0.761428i	$-0.275501\pi$
$54$		0			0
$55$	3.21608	+	8.82843i	0.433656	+	1.19042i
$56$		0			0
$57$	−6.30864	+	5.49019i	−0.835600	+	0.727193i
$58$		0			0
$59$			4.20201i			0.547055i	0.961864	+	0.273527i	$0.0881904\pi$
$59$			4.20201i			0.547055i	−0.961864	+	0.273527i	$0.911810\pi$
$60$		0			0
$61$		−	8.48528i		−	1.08643i	−0.839594	−	0.543214i	$-0.817207\pi$
$61$		−	8.48528i		−	1.08643i	0.839594	−	0.543214i	$-0.182793\pi$
$62$		0			0
$63$	−0.941967	+	6.75699i	−0.118677	+	0.851300i
$64$		0			0
$65$	−6.75699	+	2.46148i	−0.838101	+	0.305309i
$66$		0			0
$67$		−	2.27411i		−	0.277827i	−0.990305	−	0.138913i	$-0.955639\pi$
$67$		−	2.27411i		−	0.277827i	0.990305	−	0.138913i	$-0.0443609\pi$
$68$		0			0
$69$	−1.23074	−	1.41421i	−0.148164	−	0.170251i
$70$		0			0
$71$	11.8851			1.41050			0.705249	−	0.708960i	$-0.250835\pi$
$71$	11.8851			1.41050			0.705249	+	0.708960i	$0.250835\pi$
$72$		0			0
$73$		−	4.54822i		−	0.532329i	−0.963928	−	0.266164i	$-0.914244\pi$
$73$		−	4.54822i		−	0.532329i	0.963928	−	0.266164i	$-0.0857564\pi$
$74$		0			0
$75$	−1.34523	+	8.55514i	−0.155333	+	0.987862i
$76$		0			0
$77$			9.55582i			1.08899i
$78$		0			0
$79$		−	0.485281i		−	0.0545984i	−0.999627	−	0.0272992i	$-0.991309\pi$
$79$		−	0.485281i		−	0.0545984i	0.999627	−	0.0272992i	$-0.00869069\pi$
$80$		0			0
$81$	−8.65685	−	2.46148i	−0.961873	−	0.273498i
$82$		0			0
$83$	−6.94269			−0.762060			−0.381030	−	0.924563i	$-0.624431\pi$
$83$	−6.94269			−0.762060			−0.381030	+	0.924563i	$0.624431\pi$
$84$		0			0
$85$	−3.21608	+	1.17157i	−0.348832	+	0.127075i
$86$		0			0
$87$	2.27411	−	1.97908i	0.243810	−	0.212179i
$88$		0			0
$89$			8.40401i			0.890823i	0.895326	+	0.445412i	$0.146943\pi$
$89$			8.40401i			0.890823i	−0.895326	+	0.445412i	$0.853057\pi$
$90$		0			0
$91$	−7.31371			−0.766685
$92$		0			0
$93$	7.76429	+	8.92177i	0.805120	+	0.925144i
$94$		0			0
$95$	−10.1445	+	3.69552i	−1.04081	+	0.379152i
$96$		0			0
$97$		−	10.9804i		−	1.11489i	−0.830215	−	0.557444i	$-0.811782\pi$
$97$		−	10.9804i		−	1.11489i	0.830215	−	0.557444i	$-0.188218\pi$
$98$		0			0
$99$	−12.4853	−	1.74053i	−1.25482	−	0.174930i
$100$		0			0
$101$	13.6256			1.35580			0.677899	−	0.735155i	$-0.262891\pi$
$101$	13.6256			1.35580			0.677899	+	0.735155i	$0.262891\pi$
$102$		0			0
$103$	−8.70626			−0.857853			−0.428927	−	0.903339i	$-0.641108\pi$
$103$	−8.70626			−0.857853			−0.428927	+	0.903339i	$0.641108\pi$
$104$		0			0
$105$	−4.26357	+	7.70685i	−0.416081	+	0.752112i
$106$		0			0
$107$	−5.67459			−0.548584			−0.274292	−	0.961647i	$-0.588443\pi$
$107$	−5.67459			−0.548584			−0.274292	+	0.961647i	$0.588443\pi$
$108$		0			0
$109$			16.4853i			1.57900i	0.613748	+	0.789502i	$0.289661\pi$
$109$			16.4853i			1.57900i	−0.613748	+	0.789502i	$0.710339\pi$
$110$		0			0
$111$	10.1445	−	8.82843i	0.962877	−	0.837957i
$112$		0			0
$113$	−0.634051			−0.0596465			−0.0298232	−	0.999555i	$-0.509494\pi$
$113$	−0.634051			−0.0596465			−0.0298232	+	0.999555i	$0.509494\pi$
$114$		0			0
$115$	−0.828427	−	2.27411i	−0.0772512	−	0.212062i
$116$		0			0
$117$	1.33214	−	9.55582i	0.123157	−	0.883436i
$118$		0			0
$119$	−3.48106			−0.319108
$120$		0			0
$121$	−6.65685			−0.605169
$122$		0			0
$123$	2.79884	+	3.21608i	0.252362	+	0.289984i
$124$		0			0
$125$	−5.58206	+	9.68714i	−0.499275	+	0.866444i
$126$		0			0
$127$	2.27411			0.201795			0.100897	−	0.994897i	$-0.467829\pi$
$127$	2.27411			0.201795			0.100897	+	0.994897i	$0.467829\pi$
$128$		0			0
$129$	9.89949	+	11.3753i	0.871602	+	1.00154i
$130$		0			0
$131$			11.1641i			0.975413i	0.873008	+	0.487707i	$0.162166\pi$
$131$			11.1641i			0.975413i	−0.873008	+	0.487707i	$0.837834\pi$
$132$		0			0
$133$	−10.9804			−0.952119
$134$		0			0
$135$	−9.29291	−	6.97437i	−0.799806	−	0.600258i
$136$		0			0
$137$	8.02509			0.685629			0.342815	−	0.939403i	$-0.388620\pi$
$137$	8.02509			0.685629			0.342815	+	0.939403i	$0.388620\pi$
$138$		0			0
$139$	2.48528			0.210799			0.105399	−	0.994430i	$-0.466388\pi$
$139$	2.48528			0.210799			0.105399	+	0.994430i	$0.466388\pi$
$140$		0			0
$141$	1.23074	+	1.41421i	0.103647	+	0.119098i
$142$		0			0
$143$		−	13.5140i		−	1.13010i
$144$		0			0
$145$	3.65685	−	1.33214i	0.303685	−	0.110628i
$146$		0			0
$147$	2.38896	−	2.07902i	0.197038	−	0.171475i
$148$		0			0
$149$	−0.720950			−0.0590625			−0.0295313	−	0.999564i	$-0.509401\pi$
$149$	−0.720950			−0.0590625			−0.0295313	+	0.999564i	$0.509401\pi$
$150$		0			0
$151$		−	2.82843i		−	0.230174i	−0.993355	−	0.115087i	$-0.963285\pi$
$151$		−	2.82843i		−	0.230174i	0.993355	−	0.115087i	$-0.0367147\pi$
$152$		0			0
$153$	0.634051	−	4.54822i	0.0512600	−	0.367702i
$154$		0			0
$155$	5.22625	+	14.3465i	0.419783	+	1.15234i
$156$		0			0
$157$	23.2929			1.85897			0.929487	−	0.368854i	$-0.120250\pi$
$157$	23.2929			1.85897			0.929487	+	0.368854i	$0.120250\pi$
$158$		0			0
$159$	12.6060	+	14.4853i	0.999722	+	1.14876i
$160$		0			0
$161$		−	2.46148i		−	0.193992i
$162$		0			0
$163$			8.70626i			0.681927i	0.940077	+	0.340964i	$0.110753\pi$
$163$			8.70626i			0.681927i	−0.940077	+	0.340964i	$0.889247\pi$
$164$		0			0
$165$	−14.2404	−	7.87804i	−1.10861	−	0.613305i
$166$		0			0
$167$			5.04054i			0.390049i	0.980798	+	0.195024i	$0.0624786\pi$
$167$			5.04054i			0.390049i	−0.980798	+	0.195024i	$0.937521\pi$
$168$		0			0
$169$	−2.65685			−0.204373
$170$		0			0
$171$	2.00000	−	14.3465i	0.152944	−	1.09711i
$172$		0			0
$173$		−	0.262632i		−	0.0199676i	−0.999950	−	0.00998379i	$-0.996822\pi$
$173$		−	0.262632i		−	0.0199676i	0.999950	−	0.00998379i	$-0.00317799\pi$
$174$		0			0
$175$	−8.70626	+	7.31371i	−0.658132	+	0.552864i
$176$		0			0
$177$	−4.77791	−	5.49019i	−0.359130	−	0.412668i
$178$		0			0
$179$		−	7.68306i		−	0.574259i	−0.957892	−	0.287129i	$-0.907299\pi$
$179$		−	7.68306i		−	0.574259i	0.957892	−	0.287129i	$-0.0927010\pi$
$180$		0			0
$181$		−	21.6569i		−	1.60974i	−0.593450	−	0.804871i	$-0.702235\pi$
$181$		−	21.6569i		−	1.60974i	0.593450	−	0.804871i	$-0.297765\pi$
$182$		0			0
$183$	9.64823	+	11.0866i	0.713218	+	0.819542i
$184$		0			0
$185$	16.3128	−	5.94253i	1.19934	−	0.436904i
$186$		0			0
$187$		−	6.43215i		−	0.470366i
$188$		0			0
$189$	−6.45232	−	9.89949i	−0.469337	−	0.720082i
$190$		0			0
$191$	−8.40401			−0.608093			−0.304046	−	0.952657i	$-0.598338\pi$
$191$	−8.40401			−0.608093			−0.304046	+	0.952657i	$0.598338\pi$
$192$		0			0
$193$			13.6447i			0.982164i	0.871113	+	0.491082i	$0.163398\pi$
$193$			13.6447i			0.982164i	−0.871113	+	0.491082i	$0.836602\pi$
$194$		0			0
$195$	6.02959	−	10.8991i	0.431788	−	0.780503i
$196$		0			0
$197$		−	8.02509i		−	0.571764i	−0.958265	−	0.285882i	$-0.907713\pi$
$197$		−	8.02509i		−	0.571764i	0.958265	−	0.285882i	$-0.0922865\pi$
$198$		0			0
$199$		−	14.8284i		−	1.05116i	−0.850744	−	0.525580i	$-0.823848\pi$
$199$		−	14.8284i		−	1.05116i	0.850744	−	0.525580i	$-0.176152\pi$
$200$		0			0
$201$	2.58579	+	2.97127i	0.182387	+	0.209577i
$202$		0			0
$203$	3.95815			0.277808
$204$		0			0
$205$	1.88393	+	5.17157i	0.131580	+	0.361198i
$206$		0			0
$207$	3.21608	+	0.448342i	0.223533	+	0.0311619i
$208$		0			0
$209$		−	20.2891i		−	1.40342i
$210$		0			0
$211$	−1.51472			−0.104278			−0.0521388	−	0.998640i	$-0.516604\pi$
$211$	−1.51472			−0.104278			−0.0521388	+	0.998640i	$0.516604\pi$
$212$		0			0
$213$	−15.5286	+	13.5140i	−1.06400	+	0.925962i
$214$		0			0
$215$	6.66348	+	18.2919i	0.454446	+	1.24750i
$216$		0			0
$217$			15.5286i			1.05415i
$218$		0			0
$219$	5.17157	+	5.94253i	0.349463	+	0.401559i
$220$		0			0
$221$	4.92296			0.331154
$222$		0			0
$223$	10.5902			0.709172			0.354586	−	0.935023i	$-0.384622\pi$
$223$	10.5902			0.709172			0.354586	+	0.935023i	$0.384622\pi$
$224$		0			0
$225$	−7.97003	−	12.7074i	−0.531336	−	0.847161i
$226$		0			0
$227$	4.77791			0.317121			0.158561	−	0.987349i	$-0.449315\pi$
$227$	4.77791			0.317121			0.158561	+	0.987349i	$0.449315\pi$
$228$		0			0
$229$			3.31371i			0.218976i	0.993988	+	0.109488i	$0.0349211\pi$
$229$			3.31371i			0.218976i	−0.993988	+	0.109488i	$0.965079\pi$
$230$		0			0
$231$	−10.8655	−	12.4853i	−0.714897	−	0.821471i
$232$		0			0
$233$	−28.0334			−1.83653			−0.918265	−	0.395967i	$-0.870410\pi$
$233$	−28.0334			−1.83653			−0.918265	+	0.395967i	$0.870410\pi$
$234$		0			0
$235$	0.828427	+	2.27411i	0.0540406	+	0.148347i
$236$		0			0
$237$	0.551791	+	0.634051i	0.0358427	+	0.0411860i
$238$		0			0
$239$	−13.3270			−0.862050			−0.431025	−	0.902340i	$-0.641848\pi$
$239$	−13.3270			−0.862050			−0.431025	+	0.902340i	$0.641848\pi$
$240$		0			0
$241$	10.4853			0.675416			0.337708	−	0.941251i	$-0.390348\pi$
$241$	10.4853			0.675416			0.337708	+	0.941251i	$0.390348\pi$
$242$		0			0
$243$	14.1096	−	6.62724i	0.905129	−	0.425138i
$244$		0			0
$245$	3.84153	−	1.39942i	0.245426	−	0.0894055i
$246$		0			0
$247$	15.5286			0.988060
$248$		0			0
$249$	9.07107	−	7.89422i	0.574856	−	0.500276i
$250$		0			0
$251$		−	27.9721i		−	1.76559i	−0.469762	−	0.882793i	$-0.655660\pi$
$251$		−	27.9721i		−	1.76559i	0.469762	−	0.882793i	$-0.344340\pi$
$252$		0			0
$253$	4.54822			0.285944
$254$		0			0
$255$	2.86986	−	5.18759i	0.179718	−	0.324859i
$256$		0			0
$257$	−2.42742			−0.151418			−0.0757090	−	0.997130i	$-0.524122\pi$
$257$	−2.42742			−0.151418			−0.0757090	+	0.997130i	$0.524122\pi$
$258$		0			0
$259$	17.6569			1.09714
$260$		0			0
$261$	−0.720950	+	5.17157i	−0.0446257	+	0.320112i
$262$		0			0
$263$		−	27.5851i		−	1.70097i	−0.526001	−	0.850484i	$-0.676309\pi$
$263$		−	27.5851i		−	1.70097i	0.526001	−	0.850484i	$-0.323691\pi$
$264$		0			0
$265$	8.48528	+	23.2929i	0.521247	+	1.43087i
$266$		0			0
$267$	−9.55582	−	10.9804i	−0.584807	−	0.671988i
$268$		0			0
$269$	−7.68306			−0.468445			−0.234222	−	0.972183i	$-0.575254\pi$
$269$	−7.68306			−0.468445			−0.234222	+	0.972183i	$0.575254\pi$
$270$		0			0
$271$			14.1421i			0.859074i	0.903049	+	0.429537i	$0.141323\pi$
$271$			14.1421i			0.859074i	−0.903049	+	0.429537i	$0.858677\pi$
$272$		0			0
$273$	9.55582	−	8.31609i	0.578345	−	0.503312i
$274$		0			0
$275$	−13.5140	−	16.0871i	−0.814923	−	0.970087i
$276$		0			0
$277$	−16.8607			−1.01306			−0.506532	−	0.862221i	$-0.669073\pi$
$277$	−16.8607			−1.01306			−0.506532	+	0.862221i	$0.669073\pi$
$278$		0			0
$279$	−20.2891	−	2.82843i	−1.21468	−	0.169334i
$280$		0			0
$281$		−	5.94253i		−	0.354502i	−0.984166	−	0.177251i	$-0.943280\pi$
$281$		−	5.94253i		−	0.354502i	0.984166	−	0.177251i	$-0.0567204\pi$
$282$		0			0
$283$			26.1188i			1.55260i	0.630363	+	0.776300i	$0.282906\pi$
$283$			26.1188i			1.55260i	−0.630363	+	0.776300i	$0.717094\pi$
$284$		0			0
$285$	9.05247	−	16.3633i	0.536222	−	0.969280i
$286$		0			0
$287$			5.59767i			0.330420i
$288$		0			0
$289$	−14.6569			−0.862168
$290$		0			0
$291$	12.4853	+	14.3465i	0.731900	+	0.841009i
$292$		0			0
$293$		−	16.3128i		−	0.953004i	−0.879173	−	0.476502i	$-0.841904\pi$
$293$		−	16.3128i		−	0.953004i	0.879173	−	0.476502i	$-0.158096\pi$
$294$		0			0
$295$	−3.21608	−	8.82843i	−0.187247	−	0.514011i
$296$		0			0
$297$	18.2919	−	11.9223i	1.06140	−	0.691804i
$298$		0			0
$299$			3.48106i			0.201315i
$300$		0			0
$301$			19.7990i			1.14119i
$302$		0			0
$303$	−17.8027	+	15.4930i	−1.02274	+	0.890052i
$304$		0			0
$305$	6.49435	+	17.8276i	0.371866	+	1.02081i
$306$		0			0
$307$			17.8027i			1.01605i	0.861341	+	0.508027i	$0.169625\pi$
$307$			17.8027i			1.01605i	−0.861341	+	0.508027i	$0.830375\pi$
$308$		0			0
$309$	11.3753	−	9.89949i	0.647117	−	0.563163i
$310$		0			0
$311$	9.84591			0.558310			0.279155	−	0.960246i	$-0.409946\pi$
$311$	9.84591			0.558310			0.279155	+	0.960246i	$0.409946\pi$
$312$		0			0
$313$		−	24.6250i		−	1.39189i	−0.718096	−	0.695944i	$-0.754986\pi$
$313$		−	24.6250i		−	1.39189i	0.718096	−	0.695944i	$-0.245014\pi$
$314$		0			0
$315$	−3.19250	−	14.9174i	−0.179877	−	0.840500i
$316$		0			0
$317$			9.81845i			0.551459i	0.961235	+	0.275730i	$0.0889194\pi$
$317$			9.81845i			0.551459i	−0.961235	+	0.275730i	$0.911081\pi$
$318$		0			0
$319$			7.31371i			0.409489i
$320$		0			0
$321$	7.41421	−	6.45232i	0.413821	−	0.360134i
$322$		0			0
$323$	7.39104			0.411248
$324$		0			0
$325$	12.3125	−	10.3431i	0.682975	−	0.573734i
$326$		0			0
$327$	−18.7447	−	21.5391i	−1.03658	−	1.19111i
$328$		0			0
$329$			2.46148i			0.135706i
$330$		0			0
$331$	1.51472			0.0832565			0.0416282	−	0.999133i	$-0.486745\pi$
$331$	1.51472			0.0832565			0.0416282	+	0.999133i	$0.486745\pi$
$332$		0			0
$333$	−3.21608	+	23.0698i	−0.176240	+	1.26422i
$334$		0			0
$335$	1.74053	+	4.77791i	0.0950952	+	0.261045i
$336$		0			0
$337$			19.2965i			1.05114i	0.850749	+	0.525572i	$0.176149\pi$
$337$			19.2965i			1.05114i	−0.850749	+	0.525572i	$0.823851\pi$
$338$		0			0
$339$	0.828427	−	0.720950i	0.0449940	−	0.0391566i
$340$		0			0
$341$	−28.6931			−1.55382
$342$		0			0
$343$	20.0768			1.08405
$344$		0			0
$345$	3.66818	+	2.02930i	0.197488	+	0.109254i
$346$		0			0
$347$	15.2304			0.817611			0.408806	−	0.912621i	$-0.365945\pi$
$347$	15.2304			0.817611			0.408806	+	0.912621i	$0.365945\pi$
$348$		0			0
$349$		−	13.6569i		−	0.731035i	−0.930805	−	0.365517i	$-0.880892\pi$
$349$		−	13.6569i		−	0.731035i	0.930805	−	0.365517i	$-0.119108\pi$
$350$		0			0
$351$	9.12496	+	14.0000i	0.487054	+	0.747265i
$352$		0			0
$353$	26.3939			1.40481			0.702403	−	0.711780i	$-0.252111\pi$
$353$	26.3939			1.40481			0.702403	+	0.711780i	$0.252111\pi$
$354$		0			0
$355$	−24.9706	+	9.09644i	−1.32530	+	0.482789i
$356$		0			0
$357$	4.54822	−	3.95815i	0.240717	−	0.209488i
$358$		0			0
$359$	32.1741			1.69809			0.849043	−	0.528323i	$-0.177179\pi$
$359$	32.1741			1.69809			0.849043	+	0.528323i	$0.177179\pi$
$360$		0			0
$361$	4.31371			0.227037
$362$		0			0
$363$	8.69760	−	7.56921i	0.456506	−	0.397280i
$364$		0			0
$365$	3.48106	+	9.55582i	0.182207	+	0.500175i
$366$		0			0
$367$	−24.2349			−1.26505			−0.632524	−	0.774540i	$-0.717981\pi$
$367$	−24.2349			−1.26505			−0.632524	+	0.774540i	$0.717981\pi$
$368$		0			0
$369$	−7.31371	−	1.01958i	−0.380736	−	0.0530771i
$370$		0			0
$371$			25.2120i			1.30894i
$372$		0			0
$373$	10.4286			0.539971			0.269986	−	0.962864i	$-0.412981\pi$
$373$	10.4286			0.539971			0.269986	+	0.962864i	$0.412981\pi$
$374$		0			0
$375$	−3.72149	−	19.0040i	−0.192177	−	0.981360i
$376$		0			0
$377$	−5.59767			−0.288295
$378$		0			0
$379$	−15.1716			−0.779311			−0.389656	−	0.920961i	$-0.627406\pi$
$379$	−15.1716			−0.779311			−0.389656	+	0.920961i	$0.627406\pi$
$380$		0			0
$381$	−2.97127	+	2.58579i	−0.152223	+	0.132474i
$382$		0			0
$383$		−	18.5545i		−	0.948091i	−0.880500	−	0.474046i	$-0.842793\pi$
$383$		−	18.5545i		−	0.948091i	0.880500	−	0.474046i	$-0.157207\pi$
$384$		0			0
$385$	−7.31371	−	20.0768i	−0.372741	−	1.02321i
$386$		0			0
$387$	−25.8686	−	3.60625i	−1.31498	−	0.183316i
$388$		0			0
$389$	12.6060			0.639150			0.319575	−	0.947561i	$-0.396460\pi$
$389$	12.6060			0.639150			0.319575	+	0.947561i	$0.396460\pi$
$390$		0			0
$391$			1.65685i			0.0837907i
$392$		0			0
$393$	−12.6942	−	14.5866i	−0.640338	−	0.735798i
$394$		0			0
$395$	0.371418	+	1.01958i	0.0186881	+	0.0513005i
$396$		0			0
$397$	−0.551791			−0.0276936			−0.0138468	−	0.999904i	$-0.504408\pi$
$397$	−0.551791			−0.0276936			−0.0138468	+	0.999904i	$0.504408\pi$
$398$		0			0
$399$	14.3465	−	12.4853i	0.718226	−	0.625046i
$400$		0			0
$401$			25.2120i			1.25903i	0.776989	+	0.629514i	$0.216746\pi$
$401$			25.2120i			1.25903i	−0.776989	+	0.629514i	$0.783254\pi$
$402$		0			0
$403$		−	21.9607i		−	1.09394i
$404$		0			0
$405$	20.0720	−	1.45410i	0.997386	−	0.0722546i
$406$		0			0
$407$			32.6256i			1.61719i
$408$		0			0
$409$	−7.17157			−0.354611			−0.177306	−	0.984156i	$-0.556738\pi$
$409$	−7.17157			−0.354611			−0.177306	+	0.984156i	$0.556738\pi$
$410$		0			0
$411$	−10.4853	+	9.12496i	−0.517201	+	0.450101i
$412$		0			0
$413$		−	9.55582i		−	0.470211i
$414$		0			0
$415$	14.5866	−	5.31371i	0.716029	−	0.260840i
$416$		0			0
$417$	−3.24718	+	2.82590i	−0.159015	+	0.138385i
$418$		0			0
$419$		−	4.20201i		−	0.205281i	−0.994718	−	0.102641i	$-0.967271\pi$
$419$		−	4.20201i		−	0.205281i	0.994718	−	0.102641i	$-0.0327292\pi$
$420$		0			0
$421$			29.1716i			1.42174i	0.703326	+	0.710868i	$0.251698\pi$
$421$			29.1716i			1.42174i	−0.703326	+	0.710868i	$0.748302\pi$
$422$		0			0
$423$	−3.21608	−	0.448342i	−0.156371	−	0.0217991i
$424$		0			0
$425$	5.86030	−	4.92296i	0.284266	−	0.238798i
$426$		0			0
$427$			19.2965i			0.933821i
$428$		0			0
$429$	15.3661	+	17.6569i	0.741883	+	0.852481i
$430$		0			0
$431$	−21.7310			−1.04674			−0.523372	−	0.852104i	$-0.675326\pi$
$431$	−21.7310			−1.04674			−0.523372	+	0.852104i	$0.675326\pi$
$432$		0			0
$433$			29.1732i			1.40198i	0.713173	+	0.700988i	$0.247258\pi$
$433$			29.1732i			1.40198i	−0.713173	+	0.700988i	$0.752742\pi$
$434$		0			0
$435$	−3.26319	+	5.89857i	−0.156458	+	0.282815i
$436$		0			0
$437$			5.22625i			0.250006i
$438$		0			0
$439$			11.5147i			0.549568i	0.961506	+	0.274784i	$0.0886063\pi$
$439$			11.5147i			0.549568i	−0.961506	+	0.274784i	$0.911394\pi$
$440$		0			0
$441$	−0.757359	+	5.43275i	−0.0360647	+	0.258702i
$442$		0			0
$443$	−40.4650			−1.92255			−0.961275	−	0.275591i	$-0.911126\pi$
$443$	−40.4650			−1.92255			−0.961275	+	0.275591i	$0.911126\pi$
$444$		0			0
$445$	−6.43215	−	17.6569i	−0.304913	−	0.837015i
$446$		0			0
$447$	0.941967	−	0.819760i	0.0445535	−	0.0387733i
$448$		0			0
$449$			24.7897i			1.16990i	0.811070	+	0.584949i	$0.198886\pi$
$449$			24.7897i			1.16990i	−0.811070	+	0.584949i	$0.801114\pi$
$450$		0			0
$451$	−10.3431			−0.487040
$452$		0			0
$453$	3.21608	+	3.69552i	0.151104	+	0.173631i
$454$		0			0
$455$	15.3661	−	5.59767i	0.720375	−	0.262423i
$456$		0			0
$457$		−	12.8643i		−	0.601767i	−0.953661	−	0.300883i	$-0.902719\pi$
$457$		−	12.8643i		−	0.601767i	0.953661	−	0.300883i	$-0.0972815\pi$
$458$		0			0
$459$	4.34315	+	6.66348i	0.202721	+	0.311025i
$460$		0			0
$461$	−18.5486			−0.863892			−0.431946	−	0.901899i	$-0.642173\pi$
$461$	−18.5486			−0.863892			−0.431946	+	0.901899i	$0.642173\pi$
$462$		0			0
$463$	4.93839			0.229507			0.114753	−	0.993394i	$-0.463392\pi$
$463$	4.93839			0.229507			0.114753	+	0.993394i	$0.463392\pi$
$464$		0			0
$465$	−23.1412	−	12.8021i	−1.07315	−	0.593685i
$466$		0			0
$467$	8.73606			0.404257			0.202128	−	0.979359i	$-0.435214\pi$
$467$	8.73606			0.404257			0.202128	+	0.979359i	$0.435214\pi$
$468$		0			0
$469$			5.17157i			0.238801i
$470$		0			0
$471$	−30.4336	+	26.4853i	−1.40231	+	1.22038i
$472$		0			0
$473$	−36.5838			−1.68212
$474$		0			0
$475$	18.4853	−	15.5286i	0.848163	−	0.712501i
$476$		0			0
$477$	−32.9411	−	4.59220i	−1.50827	−	0.210262i
$478$		0			0
$479$	−15.3661			−0.702096			−0.351048	−	0.936357i	$-0.614175\pi$
$479$	−15.3661			−0.702096			−0.351048	+	0.936357i	$0.614175\pi$
$480$		0			0
$481$	−24.9706			−1.13856
$482$		0			0
$483$	2.79884	+	3.21608i	0.127351	+	0.146337i
$484$		0			0
$485$	8.40401	+	23.0698i	0.381607	+	1.04755i
$486$		0			0
$487$	−19.6866			−0.892086			−0.446043	−	0.895011i	$-0.647167\pi$
$487$	−19.6866			−0.892086			−0.446043	+	0.895011i	$0.647167\pi$
$488$		0			0
$489$	−9.89949	−	11.3753i	−0.447671	−	0.514408i
$490$		0			0
$491$			14.0479i			0.633974i	0.948430	+	0.316987i	$0.102671\pi$
$491$			14.0479i			0.633974i	−0.948430	+	0.316987i	$0.897329\pi$
$492$		0			0
$493$	−2.66428			−0.119993
$494$		0			0
$495$	27.5638	−	5.89897i	1.23890	−	0.265139i
$496$		0			0
$497$	−27.0279			−1.21237
$498$		0			0
$499$	−25.1127			−1.12420			−0.562099	−	0.827070i	$-0.690006\pi$
$499$	−25.1127			−1.12420			−0.562099	+	0.827070i	$0.690006\pi$
$500$		0			0
$501$	−5.73137	−	6.58579i	−0.256059	−	0.294231i
$502$		0			0
$503$			28.4818i			1.26994i	0.772537	+	0.634969i	$0.218987\pi$
$503$			28.4818i			1.26994i	−0.772537	+	0.634969i	$0.781013\pi$
$504$		0			0
$505$	−28.6274	+	10.4286i	−1.27390	+	0.464066i
$506$		0			0
$507$	3.47135	−	3.02099i	0.154168	−	0.134167i
$508$		0			0
$509$	13.6256			0.603944			0.301972	−	0.953317i	$-0.402355\pi$
$509$	13.6256			0.603944			0.301972	+	0.953317i	$0.402355\pi$
$510$		0			0
$511$			10.3431i			0.457554i
$512$		0			0
$513$	13.6997	+	21.0188i	0.604856	+	0.928002i
$514$		0			0
$515$	18.2919	−	6.66348i	0.806037	−	0.293628i
$516$		0			0
$517$	−4.54822			−0.200030
$518$		0			0
$519$	0.298627	+	0.343146i	0.0131083	+	0.0150624i
$520$		0			0
$521$			9.84591i			0.431357i	0.976464	+	0.215679i	$0.0691964\pi$
$521$			9.84591i			0.431357i	−0.976464	+	0.215679i	$0.930804\pi$
$522$		0			0
$523$		−	4.15804i		−	0.181819i	−0.995859	−	0.0909093i	$-0.971023\pi$
$523$		−	4.15804i		−	0.181819i	0.995859	−	0.0909093i	$-0.0289773\pi$
$524$		0			0
$525$	3.05919	−	19.4553i	0.133514	−	0.849100i
$526$		0			0
$527$		−	10.4525i		−	0.455318i
$528$		0			0
$529$	21.8284			0.949062
$530$		0			0
$531$	12.4853	+	1.74053i	0.541815	+	0.0755325i
$532$		0			0
$533$		−	7.91630i		−	0.342893i
$534$		0			0
$535$	11.9223	−	4.34315i	0.515448	−	0.187771i
$536$		0			0
$537$	8.73606	+	10.0384i	0.376989	+	0.433189i
$538$		0			0
$539$			7.68306i			0.330933i
$540$		0			0
$541$			16.0000i			0.687894i	0.938989	+	0.343947i	$0.111764\pi$
$541$			16.0000i			0.687894i	−0.938989	+	0.343947i	$0.888236\pi$
$542$		0			0
$543$	24.6250	+	28.2960i	1.05676	+	1.21430i
$544$		0			0
$545$	−12.6173	−	34.6356i	−0.540465	−	1.48363i
$546$		0			0
$547$		−	33.3313i		−	1.42514i	−0.701600	−	0.712571i	$-0.747530\pi$
$547$		−	33.3313i		−	1.42514i	0.701600	−	0.712571i	$-0.252470\pi$
$548$		0			0
$549$	−25.2120	−	3.51472i	−1.07602	−	0.150005i
$550$		0			0
$551$	−8.40401			−0.358023
$552$		0			0
$553$			1.10358i			0.0469291i
$554$		0			0
$555$	−14.5567	+	26.3128i	−0.617898	+	1.11692i
$556$		0			0
$557$		−	19.3743i		−	0.820914i	−0.911880	−	0.410457i	$-0.865369\pi$
$557$		−	19.3743i		−	0.820914i	0.911880	−	0.410457i	$-0.134631\pi$
$558$		0			0
$559$		−	28.0000i		−	1.18427i
$560$		0			0
$561$	7.31371	+	8.40401i	0.308785	+	0.354818i
$562$		0			0
$563$	−6.04601			−0.254809			−0.127405	−	0.991851i	$-0.540665\pi$
$563$	−6.04601			−0.254809			−0.127405	+	0.991851i	$0.540665\pi$
$564$		0			0
$565$	1.33214	−	0.485281i	0.0560437	−	0.0204159i
$566$		0			0
$567$	19.6866	+	5.59767i	0.826761	+	0.235080i
$568$		0			0
$569$			9.42359i			0.395057i	0.980297	+	0.197529i	$0.0632916\pi$
$569$			9.42359i			0.395057i	−0.980297	+	0.197529i	$0.936708\pi$
$570$		0			0
$571$	41.1127			1.72051			0.860256	−	0.509862i	$-0.170303\pi$
$571$	41.1127			1.72051			0.860256	+	0.509862i	$0.170303\pi$
$572$		0			0
$573$	10.9804	−	9.55582i	0.458712	−	0.399200i
$574$		0			0
$575$	3.48106	+	4.14386i	0.145170	+	0.172811i
$576$		0			0
$577$		−	15.5286i		−	0.646464i	−0.946320	−	0.323232i	$-0.895231\pi$
$577$		−	15.5286i		−	0.646464i	0.946320	−	0.323232i	$-0.104769\pi$
$578$		0			0
$579$	−15.5147	−	17.8276i	−0.644770	−	0.740890i
$580$		0			0
$581$	15.7884			0.655015
$582$		0			0
$583$	−46.5858			−1.92939
$584$		0			0
$585$	4.51487	+	21.0964i	0.186667	+	0.872228i
$586$		0			0
$587$	12.1689			0.502266			0.251133	−	0.967953i	$-0.419197\pi$
$587$	12.1689			0.502266			0.251133	+	0.967953i	$0.419197\pi$
$588$		0			0
$589$		−	32.9706i		−	1.35853i
$590$		0			0
$591$	9.12496	+	10.4853i	0.375351	+	0.431307i
$592$		0			0
$593$	39.3826			1.61725			0.808625	−	0.588325i	$-0.200212\pi$
$593$	39.3826			1.61725			0.808625	+	0.588325i	$0.200212\pi$
$594$		0			0
$595$	7.31371	−	2.66428i	0.299833	−	0.109225i
$596$		0			0
$597$	16.8607	+	19.3743i	0.690064	+	0.792936i
$598$		0			0
$599$	30.1350			1.23128			0.615641	−	0.788027i	$-0.288897\pi$
$599$	30.1350			1.23128			0.615641	+	0.788027i	$0.288897\pi$
$600$		0			0
$601$	30.4853			1.24352			0.621760	−	0.783208i	$-0.286418\pi$
$601$	30.4853			1.24352			0.621760	+	0.783208i	$0.286418\pi$
$602$		0			0
$603$	−6.75699	−	0.941967i	−0.275166	−	0.0383599i
$604$		0			0
$605$	13.9861	−	5.09494i	0.568615	−	0.207139i
$606$		0			0
$607$	35.2152			1.42934			0.714671	−	0.699461i	$-0.246576\pi$
$607$	35.2152			1.42934			0.714671	+	0.699461i	$0.246576\pi$
$608$		0			0
$609$	−5.17157	+	4.50063i	−0.209563	+	0.182375i
$610$		0			0
$611$		−	3.48106i		−	0.140828i
$612$		0			0
$613$	16.0804			0.649480			0.324740	−	0.945803i	$-0.394723\pi$
$613$	16.0804			0.649480			0.324740	+	0.945803i	$0.394723\pi$
$614$		0			0
$615$	−8.34184	−	4.61485i	−0.336375	−	0.186089i
$616$		0			0
$617$	31.0949			1.25183			0.625916	−	0.779890i	$-0.284725\pi$
$617$	31.0949			1.25183			0.625916	+	0.779890i	$0.284725\pi$
$618$		0			0
$619$	−14.4853			−0.582213			−0.291106	−	0.956691i	$-0.594023\pi$
$619$	−14.4853			−0.582213			−0.291106	+	0.956691i	$0.594023\pi$
$620$		0			0
$621$	−4.71179	+	3.07107i	−0.189078	+	0.123238i
$622$		0			0
$623$		−	19.1116i		−	0.765692i
$624$		0			0
$625$	4.31371	−	24.6250i	0.172548	−	0.985001i
$626$		0			0
$627$	23.0698	+	26.5090i	0.921319	+	1.05867i
$628$		0			0
$629$	−11.8851			−0.473889
$630$		0			0
$631$			26.1421i			1.04070i	0.853952	+	0.520351i	$0.174199\pi$
$631$			26.1421i			1.04070i	−0.853952	+	0.520351i	$0.825801\pi$
$632$		0			0
$633$	1.97908	−	1.72232i	0.0786612	−	0.0684560i
$634$		0			0
$635$	−4.77791	+	1.74053i	−0.189606	+	0.0690707i
$636$		0			0
$637$	−5.88036			−0.232988
$638$		0			0
$639$	4.92296	−	35.3137i	0.194749	−	1.39699i
$640$		0			0
$641$		−	24.7897i		−	0.979135i	−0.871965	−	0.489567i	$-0.837155\pi$
$641$		−	24.7897i		−	0.979135i	0.871965	−	0.489567i	$-0.162845\pi$
$642$		0			0
$643$		−	1.49376i		−	0.0589081i	−0.999566	−	0.0294540i	$-0.990623\pi$
$643$		−	1.49376i		−	0.0589081i	0.999566	−	0.0294540i	$-0.00937687\pi$
$644$		0			0
$645$	−29.5051	−	16.3227i	−1.16176	−	0.642708i
$646$		0			0
$647$		−	42.3671i		−	1.66562i	−0.553556	−	0.832812i	$-0.686729\pi$
$647$		−	42.3671i		−	1.66562i	0.553556	−	0.832812i	$-0.313271\pi$
$648$		0			0
$649$	17.6569			0.693092
$650$		0			0
$651$	−17.6569	−	20.2891i	−0.692027	−	0.795192i
$652$		0			0
$653$		−	37.5892i		−	1.47098i	−0.677535	−	0.735490i	$-0.736952\pi$
$653$		−	37.5892i		−	1.47098i	0.677535	−	0.735490i	$-0.263048\pi$
$654$		0			0
$655$	−8.54465	−	23.4558i	−0.333867	−	0.916496i
$656$		0			0
$657$	−13.5140	−	1.88393i	−0.527230	−	0.0734993i
$658$		0			0
$659$		−	0.720950i		−	0.0280842i	−0.999901	−	0.0140421i	$-0.995530\pi$
$659$		−	0.720950i		−	0.0280842i	0.999901	−	0.0140421i	$-0.00446989\pi$
$660$		0			0
$661$			28.7696i			1.11901i	0.828828	+	0.559503i	$0.189008\pi$
$661$			28.7696i			1.11901i	−0.828828	+	0.559503i	$0.810992\pi$
$662$		0			0
$663$	−6.43215	+	5.59767i	−0.249804	+	0.217395i
$664$		0			0
$665$	23.0698	−	8.40401i	0.894608	−	0.325894i
$666$		0			0
$667$		−	1.88393i		−	0.0729462i
$668$		0			0
$669$	−13.8368	+	12.0416i	−0.534960	+	0.465556i
$670$		0			0
$671$	−35.6552			−1.37645
$672$		0			0
$673$		−	5.65180i		−	0.217861i	−0.994049	−	0.108930i	$-0.965257\pi$
$673$		−	5.65180i		−	0.217861i	0.994049	−	0.108930i	$-0.0347426\pi$
$674$		0			0
$675$	24.8624	+	7.54068i	0.956954	+	0.290241i
$676$		0			0
$677$			39.3826i			1.51360i	0.653649	+	0.756798i	$0.273237\pi$
$677$			39.3826i			1.51360i	−0.653649	+	0.756798i	$0.726763\pi$
$678$		0			0
$679$			24.9706i			0.958282i
$680$		0			0
$681$	−6.24264	+	5.43275i	−0.239219	+	0.208183i
$682$		0			0
$683$	21.3533			0.817063			0.408532	−	0.912744i	$-0.366041\pi$
$683$	21.3533			0.817063			0.408532	+	0.912744i	$0.366041\pi$
$684$		0			0
$685$	−16.8607	+	6.14214i	−0.644215	+	0.234679i
$686$		0			0
$687$	−3.76787	−	4.32957i	−0.143753	−	0.165183i
$688$		0			0
$689$		−	35.6552i		−	1.35836i
$690$		0			0
$691$	12.8284			0.488016			0.244008	−	0.969773i	$-0.421538\pi$
$691$	12.8284			0.488016			0.244008	+	0.969773i	$0.421538\pi$
$692$		0			0
$693$	28.3929	+	3.95815i	1.07856	+	0.150358i
$694$		0			0
$695$	−5.22158	+	1.90215i	−0.198066	+	0.0721527i
$696$		0			0
$697$		−	3.76787i		−	0.142718i
$698$		0			0
$699$	36.6274	−	31.8755i	1.38538	−	1.20564i
$700$		0			0
$701$	2.76011			0.104248			0.0521239	−	0.998641i	$-0.483401\pi$
$701$	2.76011			0.104248			0.0521239	+	0.998641i	$0.483401\pi$
$702$		0			0
$703$	−37.4893			−1.41394
$704$		0			0
$705$	−3.66818	−	2.02930i	−0.138152	−	0.0764279i
$706$		0			0
$707$	−30.9861			−1.16535
$708$		0			0
$709$		−	20.2843i		−	0.761792i	−0.924618	−	0.380896i	$-0.875616\pi$
$709$		−	20.2843i		−	0.761792i	0.924618	−	0.380896i	$-0.124384\pi$
$710$		0			0
$711$	−1.44190	−	0.201010i	−0.0540755	−	0.00753847i
$712$		0			0
$713$	7.39104			0.276796
$714$		0			0
$715$	10.3431	+	28.3929i	0.386812	+	1.06183i
$716$		0			0
$717$	17.4125	−	15.1535i	0.650283	−	0.565917i
$718$		0			0
$719$	−28.6931			−1.07007			−0.535036	−	0.844829i	$-0.679702\pi$
$719$	−28.6931			−1.07007			−0.535036	+	0.844829i	$0.679702\pi$
$720$		0			0
$721$	19.7990			0.737353
$722$		0			0
$723$	−13.6997	+	11.9223i	−0.509497	+	0.443397i
$724$		0			0
$725$	−6.66348	+	5.59767i	−0.247476	+	0.207892i
$726$		0			0
$727$	18.9063			0.701195			0.350598	−	0.936526i	$-0.385978\pi$
$727$	18.9063			0.701195			0.350598	+	0.936526i	$0.385978\pi$
$728$		0			0
$729$	−10.8995	+	24.7022i	−0.403685	+	0.914898i
$730$		0			0
$731$		−	13.3270i		−	0.492916i
$732$		0			0
$733$	−38.8215			−1.43390			−0.716952	−	0.697123i	$-0.754463\pi$
$733$	−38.8215			−1.43390			−0.716952	+	0.697123i	$0.754463\pi$
$734$		0			0
$735$	−3.42799	+	6.19646i	−0.126443	+	0.228560i
$736$		0			0
$737$	−9.55582			−0.351993
$738$		0			0
$739$	32.8284			1.20761			0.603807	−	0.797131i	$-0.293650\pi$
$739$	32.8284			1.20761			0.603807	+	0.797131i	$0.293650\pi$
$740$		0			0
$741$	−20.2891	+	17.6569i	−0.745338	+	0.648641i
$742$		0			0
$743$		−	0.185709i		−	0.00681301i	−0.999994	−	0.00340650i	$-0.998916\pi$
$743$		−	0.185709i		−	0.00681301i	0.999994	−	0.00340650i	$-0.00108433\pi$
$744$		0			0
$745$	1.51472	−	0.551791i	0.0554950	−	0.0202161i
$746$		0			0
$747$	−2.87576	+	20.6286i	−0.105218	+	0.754761i
$748$		0			0
$749$	12.9046			0.471525
$750$		0			0
$751$		−	27.1127i		−	0.989356i	−0.869076	−	0.494678i	$-0.835286\pi$
$751$		−	27.1127i		−	0.989356i	0.869076	−	0.494678i	$-0.164714\pi$
$752$		0			0
$753$	31.8059	+	36.5474i	1.15907	+	1.33186i
$754$		0			0
$755$	2.16478	+	5.94253i	0.0787846	+	0.216271i
$756$		0			0
$757$	36.1572			1.31416			0.657078	−	0.753823i	$-0.271792\pi$
$757$	36.1572			1.31416			0.657078	+	0.753823i	$0.271792\pi$
$758$		0			0
$759$	−5.94253	+	5.17157i	−0.215700	+	0.187716i
$760$		0			0
$761$		−	4.92296i		−	0.178457i	−0.996011	−	0.0892285i	$-0.971560\pi$
$761$		−	4.92296i		−	0.178457i	0.996011	−	0.0892285i	$-0.0284401\pi$
$762$		0			0
$763$		−	37.4893i		−	1.35720i
$764$		0			0
$765$	2.14891	+	10.0411i	0.0776941	+	0.363037i
$766$		0			0
$767$			13.5140i			0.487961i
$768$		0			0
$769$	29.5980			1.06733			0.533665	−	0.845696i	$-0.320814\pi$
$769$	29.5980			1.06733			0.533665	+	0.845696i	$0.320814\pi$
$770$		0			0
$771$	3.17157	−	2.76011i	0.114221	−	0.0994028i
$772$		0			0
$773$			38.1145i			1.37088i	0.728128	+	0.685442i	$0.240391\pi$
$773$			38.1145i			1.37088i	−0.728128	+	0.685442i	$0.759609\pi$
$774$		0			0
$775$	−21.9607	−	26.1421i	−0.788853	−	0.939053i
$776$		0			0
$777$	−23.0698	+	20.0768i	−0.827624	+	0.720251i
$778$		0			0
$779$		−	11.8851i		−	0.425827i
$780$		0			0
$781$		−	49.9411i		−	1.78703i
$782$		0			0
$783$	−4.93839	−	7.57675i	−0.176484	−	0.270771i
$784$		0			0
$785$	−48.9384	+	17.8276i	−1.74669	+	0.636294i
$786$		0			0
$787$			7.60268i			0.271006i	0.990777	+	0.135503i	$0.0432651\pi$
$787$			7.60268i			0.271006i	−0.990777	+	0.135503i	$0.956735\pi$
$788$		0			0
$789$	31.3657	+	36.0416i	1.11665	+	1.28312i
$790$		0			0
$791$	1.44190			0.0512681
$792$		0			0
$793$		−	27.2893i		−	0.969072i
$794$		0			0
$795$	−37.5718	−	20.7854i	−1.33254	−	0.737182i
$796$		0			0
$797$		−	0.634051i		−	0.0224592i	−0.999937	−	0.0112296i	$-0.996425\pi$
$797$		−	0.634051i		−	0.0224592i	0.999937	−	0.0112296i	$-0.00357457\pi$
$798$		0			0
$799$		−	1.65685i		−	0.0586153i
$800$		0			0
$801$	24.9706	+	3.48106i	0.882291	+	0.122997i
$802$		0			0
$803$	−19.1116			−0.674435
$804$		0			0
$805$	1.88393	+	5.17157i	0.0663999	+	0.182274i
$806$		0			0
$807$	10.0384	−	8.73606i	0.353369	−	0.307524i
$808$		0			0
$809$		−	40.5782i		−	1.42665i	−0.700832	−	0.713326i	$-0.747188\pi$
$809$		−	40.5782i		−	1.42665i	0.700832	−	0.713326i	$-0.252812\pi$
$810$		0			0
$811$	−2.48528			−0.0872700			−0.0436350	−	0.999048i	$-0.513894\pi$
$811$	−2.48528			−0.0872700			−0.0436350	+	0.999048i	$0.513894\pi$
$812$		0			0
$813$	−16.0804	−	18.4776i	−0.563964	−	0.648037i
$814$		0			0
$815$	−6.66348	−	18.2919i	−0.233412	−	0.640737i
$816$		0			0
$817$		−	42.0375i		−	1.47071i
$818$		0			0
$819$	−3.02944	+	21.7310i	−0.105857	+	0.759342i
$820$		0			0
$821$	−31.4532			−1.09772			−0.548862	−	0.835913i	$-0.684939\pi$
$821$	−31.4532			−1.09772			−0.548862	+	0.835913i	$0.684939\pi$
$822$		0			0
$823$	48.0795			1.67595			0.837973	−	0.545711i	$-0.183740\pi$
$823$	48.0795			1.67595			0.837973	+	0.545711i	$0.183740\pi$
$824$		0			0
$825$	35.9487	+	5.65265i	1.25157	+	0.196800i
$826$		0			0
$827$	−17.7666			−0.617806			−0.308903	−	0.951094i	$-0.599962\pi$
$827$	−17.7666			−0.617806			−0.308903	+	0.951094i	$0.599962\pi$
$828$		0			0
$829$			10.8284i			0.376087i	0.982161	+	0.188043i	$0.0602146\pi$
$829$			10.8284i			0.376087i	−0.982161	+	0.188043i	$0.939785\pi$
$830$		0			0
$831$	22.0296	−	19.1716i	0.764199	−	0.665054i
$832$		0			0
$833$	−2.79884			−0.0969739
$834$		0			0
$835$	−3.85786	−	10.5902i	−0.133507	−	0.366489i
$836$		0			0
$837$	29.7250	−	19.3743i	1.02745	−	0.669673i
$838$		0			0
$839$	5.52021			0.190579			0.0952894	−	0.995450i	$-0.469622\pi$
$839$	5.52021			0.190579			0.0952894	+	0.995450i	$0.469622\pi$
$840$		0			0
$841$	−25.9706			−0.895537
$842$		0			0
$843$	6.75699	+	7.76429i	0.232723	+	0.267417i
$844$		0			0
$845$	5.58206	−	2.03347i	0.192029	−	0.0699534i
$846$		0			0
$847$	15.1384			0.520162
$848$		0			0
$849$	−29.6985	−	34.1258i	−1.01925	−	1.17120i
$850$		0			0
$851$		−	8.40401i		−	0.288086i
$852$		0			0
$853$	6.98394			0.239126			0.119563	−	0.992827i	$-0.461851\pi$
$853$	6.98394			0.239126			0.119563	+	0.992827i	$0.461851\pi$
$854$		0			0
$855$	6.77836	+	31.6729i	0.231815	+	1.08319i
$856$		0			0
$857$	27.1367			0.926973			0.463486	−	0.886104i	$-0.346598\pi$
$857$	27.1367			0.926973			0.463486	+	0.886104i	$0.346598\pi$
$858$		0			0
$859$	−32.1421			−1.09668			−0.548338	−	0.836257i	$-0.684739\pi$
$859$	−32.1421			−1.09668			−0.548338	+	0.836257i	$0.684739\pi$
$860$		0			0
$861$	−6.36486	−	7.31371i	−0.216914	−	0.249251i
$862$		0			0
$863$			32.8113i			1.11691i	0.829535	+	0.558455i	$0.188606\pi$
$863$			32.8113i			1.11691i	−0.829535	+	0.558455i	$0.811394\pi$
$864$		0			0
$865$	0.201010	+	0.551791i	0.00683455	+	0.0187615i
$866$		0			0
$867$	19.1501	−	16.6656i	0.650372	−	0.565995i
$868$		0			0
$869$	−2.03916			−0.0691736
$870$		0			0
$871$		−	7.31371i		−	0.247816i
$872$		0			0
$873$	−32.6256	−	4.54822i	−1.10421	−	0.153934i
$874$		0			0
$875$	12.6942	−	22.0296i	0.429143	−	0.744737i
$876$		0			0
$877$	−33.4929			−1.13098			−0.565488	−	0.824757i	$-0.691312\pi$
$877$	−33.4929			−1.13098			−0.565488	+	0.824757i	$0.691312\pi$
$878$		0			0
$879$	18.5486	+	21.3137i	0.625627	+	0.718894i
$880$		0			0
$881$		−	12.3074i		−	0.414647i	−0.978272	−	0.207323i	$-0.933525\pi$
$881$		−	12.3074i		−	0.414647i	0.978272	−	0.207323i	$-0.0664752\pi$
$882$		0			0
$883$			12.4741i			0.419788i	0.977724	+	0.209894i	$0.0673119\pi$
$883$			12.4741i			0.419788i	−0.977724	+	0.209894i	$0.932688\pi$
$884$		0			0
$885$	14.2404	+	7.87804i	0.478686	+	0.264817i
$886$		0			0
$887$			37.6662i			1.26471i	0.774680	+	0.632353i	$0.217911\pi$
$887$			37.6662i			1.26471i	−0.774680	+	0.632353i	$0.782089\pi$
$888$		0			0
$889$	−5.17157			−0.173449
$890$		0			0
$891$	−10.3431	+	36.3762i	−0.346508	+	1.21865i
$892$		0			0
$893$		−	5.22625i		−	0.174890i
$894$		0			0
$895$	5.88036	+	16.1421i	0.196559	+	0.539572i
$896$		0			0
$897$	−3.95815	−	4.54822i	−0.132159	−	0.151861i
$898$		0			0
$899$			11.8851i			0.396389i
$900$		0			0
$901$		−	16.9706i		−	0.565371i
$902$		0			0
$903$	−22.5125	−	25.8686i	−0.749170	−	0.860854i
$904$		0			0
$905$	16.5754	+	45.5011i	0.550986	+	1.51251i
$906$		0			0
$907$		−	46.1956i		−	1.53390i	−0.641707	−	0.766950i	$-0.721774\pi$
$907$		−	46.1956i		−	1.53390i	0.641707	−	0.766950i	$-0.278226\pi$
$908$		0			0
$909$	5.64391	−	40.4853i	0.187197	−	1.34281i
$910$		0			0
$911$	28.6931			0.950645			0.475322	−	0.879812i	$-0.342331\pi$
$911$	28.6931			0.950645			0.475322	+	0.879812i	$0.342331\pi$
$912$		0			0
$913$			29.1732i			0.965493i
$914$		0			0
$915$	−28.7562	−	15.9084i	−0.950652	−	0.525917i
$916$		0			0
$917$		−	25.3884i		−	0.838400i
$918$		0			0
$919$			22.1421i			0.730402i	0.930929	+	0.365201i	$0.119000\pi$
$919$			22.1421i			0.730402i	−0.930929	+	0.365201i	$0.881000\pi$
$920$		0			0
$921$	−20.2426	−	23.2603i	−0.667018	−	0.766454i
$922$		0			0
$923$	38.2233			1.25813
$924$		0			0
$925$	−29.7250	+	24.9706i	−0.977353	+	0.821027i
$926$		0			0
$927$	−3.60625	+	25.8686i	−0.118445	+	0.849637i
$928$		0			0
$929$			56.3666i			1.84933i	0.380784	+	0.924664i	$0.375654\pi$
$929$			56.3666i			1.84933i	−0.380784	+	0.924664i	$0.624346\pi$
$930$		0			0
$931$	−8.82843			−0.289340
$932$		0			0
$933$	−12.8643	+	11.1953i	−0.421158	+	0.366519i
$934$		0			0
$935$	4.92296	+	13.5140i	0.160998	+	0.441954i
$936$		0			0
$937$			32.9411i			1.07614i	0.842900	+	0.538070i	$0.180846\pi$
$937$			32.9411i			1.07614i	−0.842900	+	0.538070i	$0.819154\pi$
$938$		0			0
$939$	28.0000	+	32.1741i	0.913745	+	1.04996i
$940$		0			0
$941$	−3.18243			−0.103744			−0.0518721	−	0.998654i	$-0.516519\pi$
$941$	−3.18243			−0.103744			−0.0518721	+	0.998654i	$0.516519\pi$
$942$		0			0
$943$	2.66428			0.0867610
$944$		0			0
$945$	21.1331	+	15.8605i	0.687460	+	0.515941i
$946$		0			0
$947$	36.5068			1.18631			0.593156	−	0.805087i	$-0.297882\pi$
$947$	36.5068			1.18631			0.593156	+	0.805087i	$0.297882\pi$
$948$		0			0
$949$		−	14.6274i		−	0.474826i
$950$		0			0
$951$	−11.1641	−	12.8284i	−0.362021	−	0.415990i
$952$		0			0
$953$	−39.9079			−1.29274			−0.646371	−	0.763023i	$-0.723714\pi$
$953$	−39.9079			−1.29274			−0.646371	+	0.763023i	$0.723714\pi$
$954$		0			0
$955$	17.6569	−	6.43215i	0.571362	−	0.208140i
$956$		0			0
$957$	−8.31609	−	9.55582i	−0.268821	−	0.308896i
$958$		0			0
$959$	−18.2499			−0.589321
$960$		0			0
$961$	−15.6274			−0.504110
$962$		0			0
$963$	−2.35049	+	16.8607i	−0.0757436	+	0.543329i
$964$		0			0
$965$	−10.4432	−	28.6675i	−0.336177	−	0.922838i
$966$		0			0
$967$	−51.8474			−1.66730			−0.833650	−	0.552293i	$-0.813753\pi$
$967$	−51.8474			−1.66730			−0.833650	+	0.552293i	$0.813753\pi$
$968$		0			0
$969$	−9.65685	+	8.40401i	−0.310223	+	0.269976i
$970$		0			0
$971$			48.2612i			1.54878i	0.632711	+	0.774388i	$0.281942\pi$
$971$			48.2612i			1.54878i	−0.632711	+	0.774388i	$0.718058\pi$
$972$		0			0
$973$	−5.65180			−0.181188
$974$		0			0
$975$	−4.32635	+	27.5140i	−0.138554	+	0.881152i
$976$		0			0
$977$	13.7766			0.440753			0.220376	−	0.975415i	$-0.429271\pi$
$977$	13.7766			0.440753			0.220376	+	0.975415i	$0.429271\pi$
$978$		0			0
$979$	35.3137			1.12863
$980$		0			0
$981$	48.9822	+	6.82843i	1.56388	+	0.218015i
$982$		0			0
$983$		−	1.97908i		−	0.0631227i	−0.999502	−	0.0315613i	$-0.989952\pi$
$983$		−	1.97908i		−	0.0631227i	0.999502	−	0.0315613i	$-0.0100480\pi$
$984$		0			0
$985$	6.14214	+	16.8607i	0.195705	+	0.537228i
$986$		0			0
$987$	−2.79884	−	3.21608i	−0.0890879	−	0.102369i
$988$		0			0
$989$	9.42359			0.299653
$990$		0			0
$991$			19.7990i			0.628936i	0.949268	+	0.314468i	$0.101826\pi$
$991$			19.7990i			0.628936i	−0.949268	+	0.314468i	$0.898174\pi$
$992$		0			0
$993$	−1.97908	+	1.72232i	−0.0628041	+	0.0546561i
$994$		0			0
$995$	11.3492	+	31.1546i	0.359793	+	0.987666i
$996$		0			0
$997$	12.3125			0.389941			0.194971	−	0.980809i	$-0.437539\pi$
$997$	12.3125			0.389941			0.194971	+	0.980809i	$0.437539\pi$
$998$		0			0
$999$	−22.0296	−	33.7990i	−0.696986	−	1.06935i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	480.2.m.b.239.3		16
3.2	odd	2	inner	480.2.m.b.239.16		16
4.3	odd	2		120.2.m.b.59.9	yes	16
5.2	odd	4		2400.2.b.i.2351.11		16
5.3	odd	4		2400.2.b.i.2351.6		16
5.4	even	2	inner	480.2.m.b.239.13		16
8.3	odd	2	inner	480.2.m.b.239.4		16
8.5	even	2		120.2.m.b.59.11	yes	16
12.11	even	2		120.2.m.b.59.7	yes	16
15.2	even	4		2400.2.b.i.2351.9		16
15.8	even	4		2400.2.b.i.2351.8		16
15.14	odd	2	inner	480.2.m.b.239.2		16
20.3	even	4		600.2.b.i.251.2		16
20.7	even	4		600.2.b.i.251.15		16
20.19	odd	2		120.2.m.b.59.8	yes	16
24.5	odd	2		120.2.m.b.59.5	✓	16
24.11	even	2	inner	480.2.m.b.239.15		16
40.3	even	4		2400.2.b.i.2351.5		16
40.13	odd	4		600.2.b.i.251.14		16
40.19	odd	2	inner	480.2.m.b.239.14		16
40.27	even	4		2400.2.b.i.2351.12		16
40.29	even	2		120.2.m.b.59.6	yes	16
40.37	odd	4		600.2.b.i.251.3		16
60.23	odd	4		600.2.b.i.251.16		16
60.47	odd	4		600.2.b.i.251.1		16
60.59	even	2		120.2.m.b.59.10	yes	16
120.29	odd	2		120.2.m.b.59.12	yes	16
120.53	even	4		600.2.b.i.251.4		16
120.59	even	2	inner	480.2.m.b.239.1		16
120.77	even	4		600.2.b.i.251.13		16
120.83	odd	4		2400.2.b.i.2351.7		16
120.107	odd	4		2400.2.b.i.2351.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.m.b.59.5	✓	16	24.5	odd	2
120.2.m.b.59.6	yes	16	40.29	even	2
120.2.m.b.59.7	yes	16	12.11	even	2
120.2.m.b.59.8	yes	16	20.19	odd	2
120.2.m.b.59.9	yes	16	4.3	odd	2
120.2.m.b.59.10	yes	16	60.59	even	2
120.2.m.b.59.11	yes	16	8.5	even	2
120.2.m.b.59.12	yes	16	120.29	odd	2
480.2.m.b.239.1		16	120.59	even	2	inner
480.2.m.b.239.2		16	15.14	odd	2	inner
480.2.m.b.239.3		16	1.1	even	1	trivial
480.2.m.b.239.4		16	8.3	odd	2	inner
480.2.m.b.239.13		16	5.4	even	2	inner
480.2.m.b.239.14		16	40.19	odd	2	inner
480.2.m.b.239.15		16	24.11	even	2	inner
480.2.m.b.239.16		16	3.2	odd	2	inner
600.2.b.i.251.1		16	60.47	odd	4
600.2.b.i.251.2		16	20.3	even	4
600.2.b.i.251.3		16	40.37	odd	4
600.2.b.i.251.4		16	120.53	even	4
600.2.b.i.251.13		16	120.77	even	4
600.2.b.i.251.14		16	40.13	odd	4
600.2.b.i.251.15		16	20.7	even	4
600.2.b.i.251.16		16	60.23	odd	4
2400.2.b.i.2351.5		16	40.3	even	4
2400.2.b.i.2351.6		16	5.3	odd	4
2400.2.b.i.2351.7		16	120.83	odd	4
2400.2.b.i.2351.8		16	15.8	even	4
2400.2.b.i.2351.9		16	15.2	even	4
2400.2.b.i.2351.10		16	120.107	odd	4
2400.2.b.i.2351.11		16	5.2	odd	4
2400.2.b.i.2351.12		16	40.27	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 480 = 2^{5} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	480.m (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.30656 + 1.13705i) q^{3} +(-2.10100 + 0.765367i) q^{5} -2.27411 q^{7} +(0.414214 - 2.97127i) q^{9} -4.20201i q^{11} +3.21608 q^{13} +(1.87483 - 3.38896i) q^{15} +1.53073 q^{17} +4.82843 q^{19} +(2.97127 - 2.58579i) q^{21} +1.08239i q^{23} +(3.82843 - 3.21608i) q^{25} +(2.83730 + 4.35313i) q^{27} -1.74053 q^{29} -6.82843i q^{31} +(4.77791 + 5.49019i) q^{33} +(4.77791 - 1.74053i) q^{35} -7.76429 q^{37} +(-4.20201 + 3.65685i) q^{39} -2.46148i q^{41} -8.70626i q^{43} +(1.40385 + 6.55967i) q^{45} -1.08239i q^{47} -1.82843 q^{49} +(-2.00000 + 1.74053i) q^{51} -11.0866i q^{53} +(3.21608 + 8.82843i) q^{55} +(-6.30864 + 5.49019i) q^{57} +4.20201i q^{59} -8.48528i q^{61} +(-0.941967 + 6.75699i) q^{63} +(-6.75699 + 2.46148i) q^{65} -2.27411i q^{67} +(-1.23074 - 1.41421i) q^{69} +11.8851 q^{71} -4.54822i q^{73} +(-1.34523 + 8.55514i) q^{75} +9.55582i q^{77} -0.485281i q^{79} +(-8.65685 - 2.46148i) q^{81} -6.94269 q^{83} +(-3.21608 + 1.17157i) q^{85} +(2.27411 - 1.97908i) q^{87} +8.40401i q^{89} -7.31371 q^{91} +(7.76429 + 8.92177i) q^{93} +(-10.1445 + 3.69552i) q^{95} -10.9804i q^{97} +(-12.4853 - 1.74053i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{9} + 32 q^{19} + 16 q^{25} + 16 q^{49} - 32 q^{51} - 32 q^{75} - 48 q^{81} + 64 q^{91} - 64 q^{99}+O(q^{100}) \) 16 * q - 16 * q^9 + 32 * q^19 + 16 * q^25 + 16 * q^49 - 32 * q^51 - 32 * q^75 - 48 * q^81 + 64 * q^91 - 64 * q^99

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